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arXiv · 2002.07887

Singular radial solutions for the Lin-Ni-Takagi equation

Juraj Foldes·Jean-Baptiste Casteras
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Abstract

We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension $N\geq 3$. It is shown that for any ball and any $k \geq 0$, there is a singular solution that satisfies Neumann boundary condition and oscillates at least $k$ times around the constant equilibrium. Moreover, we show that the Morse index of the singular solution is finite or infinite if the exponent is respectively larger or smaller than the Joseph--Lundgren exponent.

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Juraj Foldes, Jean-Baptiste Casteras. 2020-02-18. Singular radial solutions for the Lin-Ni-Takagi equation. https://arxiv.org/abs/2002.07887

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